Intersections then enclosed area

Practise intersections then enclosed area with an original VectorPaths question, worked explanation and related VCE Methods practice.

5 practice marks

Original practice question

The curves are $y=6x-x^2$ and $y=x$. (a) Find their intersection coordinates. [2 marks] (b) Find the exact enclosed area. [3 marks]

Worked explanation

• Part (a)

  $6x-x^2=x$ gives $x(5-x)=0$, so $x=0,5$; use $y=x$ for the ordinates.

• Part (b)

  The parabola is above the line between 0 and 5. Area $=\int_0^5(5x-x^2)\,dx=[5x^2/2-x^3/3]_0^5=125/6$.

(a) $(0,0)$ and $(5,5)$.; (b) $125/6$ square units.

Original VectorPaths practice; not an official VCAA question or marking rubric.